Transport parameters in neutron stars from in-medium NN cross sections

We present a numerical study of shear viscosity and thermal conductivity of symmetric nuclear matter, pure neutron matter and $\beta$-stable nuclear matter, in the framework of the Brueckner theory. The calculation of in-medium cross sections and nucleon effective masses is performed with a consistent two and three body interaction. The investigation covers a wide baryon density range as requested in the applications to neutron stars. The results for the transport coefficients in $\beta$-stable nuclear matter are used to make preliminary predictions on the damping time scales of non radial modes in neutron stars.